Glycerol Modulates Water Permeation through ... - Semantic Scholar
Glycerol Modulates Water Permeation through Escherichia coli Aquaglyceroporin GlpF Liao Y. Chen1† 1
Department of Physics, University of Texas at San Antonio, One UTSA Circle, San Antonio, Texas 78249 USA
†
To whom correspondence should be addressed: Liao Y. Chen Department of Physics One UTSA Circle, San Antonio Texas 78249, USA Tel: (210)458-5457 Email: [email protected]
1
ABSTRACT Among aquaglyceroporins that transport both water and glycerol across the cell membrane, Escherichia coli glycerol uptake facilitator (GlpF) is the most thoroughly studied. However, one question remains: Does glycerol modulate water permeation? This study answers this fundamental question by determining the chemical-potential profile of glycerol along the permeation path through GlpF’s conducting pore. There is a deep well near the Asn-Pro-Ala (NPA) motifs (dissociation constant 14 µM) and a barrier near the selectivity filter (10.1 kcal/mol above the well bottom). This profile owes its existence to GlpF’s perfect steric arrangement: The glycerol-protein van der Waals interactions are attractive near the NPA but repulsive elsewhere in the conducting pore. In light of the single-file nature of waters and glycerols lining up in GlpF’s amphipathic pore, it leads to the following conclusion: Glycerol modulates water permeation in the µM range. At mM concentrations, GlpF is glycerol-saturated and a glycerol dwelling in the well occludes the conducting pore. Therefore, water permeation is fully correlated to glycerol dissociation that has an Arrhenius activation barrier of 6.5 kcal/mol. Validation of this theory is based on the existent in vitro data, some of which have not been given the proper attention they deserved: The Arrhenius activation barriers were found to be 7 kcal/mol for water permeation and 9.6 kcal/mol for glycerol permeation; The presence of up to 100 mM glycerol did not affect the kinetics of water transport with very low permeability, in apparent contradiction with the existent theories that predicted high permeability (0 M glycerol).
KEYWORDS Aquaporin Aquaglyceroporin water-transport regulation glycerol-protein interaction chemical potential
2
INTRODUCTION Escherichia coli aquaglyceroporin GlpF is a member of the membrane proteins responsible for water and solute transport across the cell membrane 1-6. Among the aquaglyceroporin sub-family of proteins that conduct both water and glycerol, GlpF is the most thoroughly studied, both in vitro 7-19 and in silico 18, 20-29. There is no controversy over the science that GlpF conducts both water and glycerol and how the amphipathic pore of GlpF selectively facilitates the passage of waters and glycerols lining up in a single file through the conducting channel 17, 18, 20, 21. However, one fundamental question remains: Does glycerol modulate water permeation through GlpF? And, related to this question, there are some unsolved issues about water permeation through this protein’s conducting pore: The in vitro data indicate that GlpF is much less permeable to water than Escherichia coli aquaporin Z (AQPZ) and other water-selective aquaporins 13, 14, 30, but theoretical studies predict that GlpF is more permeable than AQPZ etc. 23, 31; The in vitro experiments show that water permeation has an Arrhenius activation barrier that is about 7 kcal/mol 13, but the theoretical studies all give a rather flat free-energy profile throughout the permeation channel of GlpF20, 27. While the in vitro experiments indicate that the presence of up to 100 mM glycerol does not affect the kinetics of water transport 13, all in silico studies are limited to 0 M glycerol concentration. All these problems can be resolved once we have an accurate determination of the chemical potential of glycerol as a function of its center-of-mass coordinates along a path leading from the periplasm to the entry vestibule of GlpF, through the channel, to the cytoplasm. This chemicalpotential profile, considered on the basis of the structure information available in the literature 17, 18, can ascertain the conclusion that glycerol strongly modulates water permeation through GlpF. Inside the GlpF channel, waters and glycerols line up in a single file, occluding one another from occupying the same z-coordinate. (The z-axis is chosen as normal to the membrane-water interface, pointing from the periplasm to the cytoplasm.) Therefore, waters and glycerols permeate through the amphipathic pore of GlpF in a concerted, collective diffusion, driven or not driven by the osmotic pressure. If a deep enough chemical-potential well exists inside the channel (where the chemical potential
3
is lower than the periplasm/cytoplasm bulk level), a glycerol molecule will be bound there, with a probability determined by the glycerol concentration and the dissociation constant. The bound glycerol will occlude permeation of waters and other glycerols through the channel. GlpF will switch between being open and closed to water permeation as a glycerol is dissociated from and bound to the binding site inside the protein’s conducting pore. Therefore, such a chemical-potential profile means that glycerol modulates water permeation through GlpF in the glycerol concentration range around the dissociation constant. In order to produce an accurate chemical-potential profile of glycerol, I conducted a total of 899 ns equilibrium and non-equilibrium molecular dynamics (MD) simulations, which amounts to about 10 times the computing efforts invested on GlpF in a published work of the current literature. The nonequilibrium MD simulations include three sets of steered molecular dynamics (SMD) 32-34 runs and two MD runs under pressure gradients. The accuracy of the chemical-potential estimation was ascertained by the agreement between the non-equilibrium SMD approach and the equilibrium adaptive biasing force (ABF) approach 24, 35. Briefly, in this in silico study, glycerol is found to have a deep chemical-potential well in the GlpF channel near the Asn-Pro-Ala (NPA) motifs that is 6.5 kcal/mol below its chemical potential in the bulk of periplasm/cytoplasm, which corresponds to a dissociation constant of 14 µM. Glycerol binding to or dissociating from this binding site strongly modulates water permeation through the GlpF pore. There are two chemical-potential barriers separating the glycerol binding site from the periplasm and cytoplasm bulk regions; The barrier at the selectivity filter (SF) between the binding site and the periplasm is 10.1 kcal/mol, and the barrier between the NPA and the cytoplasm stands at 4.6 kcal/mol above the bottom of the chemical-potential well. This chemical-potential profile, considered in the context of the structural characteristics of GlpF, leads to a new theory of glycerol modulated water permeation through GlpF that is in agreement with the in vitro results in the current literature. It also harmonizes the existent theoretical results at 0 M glycerol concentration with the in vitro experiments at up to 100 mM concentrations of
4
glycerol. Furthermore, it could be fully validated by future in vitro experiments measuring the glycerolGlpF dissociation constant and the water permeability in the µM range of glycerol concentration.
RESULTS AND DISCUSSION Chemical-potential profile of glycerol. Shown in Fig. 1 is the chemical potential of glycerol as a function of its center-of-mass position along a path leading from the periplasm to the entry vestibule of GlpF, through the channel, to the cytoplasm. Inside the channel, waters and glycerols line up in a single file, occluding one another from occupying the same z-coordinate. Outside the channel, farther away from the protein, there is more and more space for multiple waters and glycerols to occupy the same zcoordinate. In the single-file region, the chemical-potential is along the most probable path (minimal freeenergy path, plotted in red in Fig. 1). In the non-single-file regions, the chemical potential curves (green) in Fig. 1 are along two straight lines leading from the periplasm to the channel entrance and from the channel exit to the cytoplasm. It needs to be noted here that chemical potential is not exactly identical to the potential of mean force (PMF) used in, e.g., Refs. 25, 31. (See Eq. (2) in the next section.) In the nonsingle-file regions outside the conducting pore, there are many (infinite) possible paths for a glycerol to dissociate from GlpF. The PMF, being a function of only the z-coordinate of the glycerol’s center of mass, necessarily involves the information of the glycerol and protein concentrations. In contrast, the chemical potential is computed here as a function of the glycerol’s center-of-mass position (x-, y-, and zcoordinates) along two chosen straight lines leading from the protein to the periplasm and to the cytoplasm, respectively. It does not incorporate the concentration-dependence (namely, the entropic contributions) here. Considering this chemical potential (the standard free energy) along with the concentration terms36, 37, one can show that the absolute binding free-energy of glycerol is equal to the chemical-potential difference between the apo state ( z = 30 Å ) and the bound state ( z = 6.5 Å ): Eb = −6.5 ± 1.5 kcal/mol. Correspondingly, the dissociation constant of glycerol from GlpF
5
is kd = exp[ Eb / kBT ] ~ 14 µM. It should be emphasized that the binding site is in the single-file region. Therefore, water permeation through GlpF is modulated by the glycerol concentration in the µM range because a glycerol bound inside GlpF occludes the conducting channel. The inhibitory concentration at half maximum (IC50) is approximately 14 µM. Direct validation of this theory will require in vitro measurements of the dissociation constant of the glycerol-GlpF complex, which is currently unavailable in the literature. However, there are in vitro data available that validate the biophysical implications of this theory. Discussed below are the six implications of the chemical-potential profile given in Fig. 1. First, binding sites of glycerol in GlpF’s pore. The chemical-potential landscape (Fig. 1, top panel) corresponds well with the pore radius of GlpF along the channel (Fig. 1, middle and bottom panels). Where there is a maximum in pore radius, there is a minimum in chemical potential. There are three chemical-potential minima in the single-file region---one in the SF region and two in the NPA region. The locations of these minima are in agreement of the structural studies of GlpF that show a glycerol at the SF and another at the NPA 17, 18. The two minima near the NPA are both far below the bulk chemicalpotential level ( < −5 kcal/mol). They are separated from one another by a very low barrier (
Department of Physics, University of Texas at San Antonio, One UTSA Circle, San Antonio, Texas 78249 USA
†
To whom correspondence should be addressed: Liao Y. Chen Department of Physics One UTSA Circle, San Antonio Texas 78249, USA Tel: (210)458-5457 Email: [email protected]
1
ABSTRACT Among aquaglyceroporins that transport both water and glycerol across the cell membrane, Escherichia coli glycerol uptake facilitator (GlpF) is the most thoroughly studied. However, one question remains: Does glycerol modulate water permeation? This study answers this fundamental question by determining the chemical-potential profile of glycerol along the permeation path through GlpF’s conducting pore. There is a deep well near the Asn-Pro-Ala (NPA) motifs (dissociation constant 14 µM) and a barrier near the selectivity filter (10.1 kcal/mol above the well bottom). This profile owes its existence to GlpF’s perfect steric arrangement: The glycerol-protein van der Waals interactions are attractive near the NPA but repulsive elsewhere in the conducting pore. In light of the single-file nature of waters and glycerols lining up in GlpF’s amphipathic pore, it leads to the following conclusion: Glycerol modulates water permeation in the µM range. At mM concentrations, GlpF is glycerol-saturated and a glycerol dwelling in the well occludes the conducting pore. Therefore, water permeation is fully correlated to glycerol dissociation that has an Arrhenius activation barrier of 6.5 kcal/mol. Validation of this theory is based on the existent in vitro data, some of which have not been given the proper attention they deserved: The Arrhenius activation barriers were found to be 7 kcal/mol for water permeation and 9.6 kcal/mol for glycerol permeation; The presence of up to 100 mM glycerol did not affect the kinetics of water transport with very low permeability, in apparent contradiction with the existent theories that predicted high permeability (0 M glycerol).
KEYWORDS Aquaporin Aquaglyceroporin water-transport regulation glycerol-protein interaction chemical potential
2
INTRODUCTION Escherichia coli aquaglyceroporin GlpF is a member of the membrane proteins responsible for water and solute transport across the cell membrane 1-6. Among the aquaglyceroporin sub-family of proteins that conduct both water and glycerol, GlpF is the most thoroughly studied, both in vitro 7-19 and in silico 18, 20-29. There is no controversy over the science that GlpF conducts both water and glycerol and how the amphipathic pore of GlpF selectively facilitates the passage of waters and glycerols lining up in a single file through the conducting channel 17, 18, 20, 21. However, one fundamental question remains: Does glycerol modulate water permeation through GlpF? And, related to this question, there are some unsolved issues about water permeation through this protein’s conducting pore: The in vitro data indicate that GlpF is much less permeable to water than Escherichia coli aquaporin Z (AQPZ) and other water-selective aquaporins 13, 14, 30, but theoretical studies predict that GlpF is more permeable than AQPZ etc. 23, 31; The in vitro experiments show that water permeation has an Arrhenius activation barrier that is about 7 kcal/mol 13, but the theoretical studies all give a rather flat free-energy profile throughout the permeation channel of GlpF20, 27. While the in vitro experiments indicate that the presence of up to 100 mM glycerol does not affect the kinetics of water transport 13, all in silico studies are limited to 0 M glycerol concentration. All these problems can be resolved once we have an accurate determination of the chemical potential of glycerol as a function of its center-of-mass coordinates along a path leading from the periplasm to the entry vestibule of GlpF, through the channel, to the cytoplasm. This chemicalpotential profile, considered on the basis of the structure information available in the literature 17, 18, can ascertain the conclusion that glycerol strongly modulates water permeation through GlpF. Inside the GlpF channel, waters and glycerols line up in a single file, occluding one another from occupying the same z-coordinate. (The z-axis is chosen as normal to the membrane-water interface, pointing from the periplasm to the cytoplasm.) Therefore, waters and glycerols permeate through the amphipathic pore of GlpF in a concerted, collective diffusion, driven or not driven by the osmotic pressure. If a deep enough chemical-potential well exists inside the channel (where the chemical potential
3
is lower than the periplasm/cytoplasm bulk level), a glycerol molecule will be bound there, with a probability determined by the glycerol concentration and the dissociation constant. The bound glycerol will occlude permeation of waters and other glycerols through the channel. GlpF will switch between being open and closed to water permeation as a glycerol is dissociated from and bound to the binding site inside the protein’s conducting pore. Therefore, such a chemical-potential profile means that glycerol modulates water permeation through GlpF in the glycerol concentration range around the dissociation constant. In order to produce an accurate chemical-potential profile of glycerol, I conducted a total of 899 ns equilibrium and non-equilibrium molecular dynamics (MD) simulations, which amounts to about 10 times the computing efforts invested on GlpF in a published work of the current literature. The nonequilibrium MD simulations include three sets of steered molecular dynamics (SMD) 32-34 runs and two MD runs under pressure gradients. The accuracy of the chemical-potential estimation was ascertained by the agreement between the non-equilibrium SMD approach and the equilibrium adaptive biasing force (ABF) approach 24, 35. Briefly, in this in silico study, glycerol is found to have a deep chemical-potential well in the GlpF channel near the Asn-Pro-Ala (NPA) motifs that is 6.5 kcal/mol below its chemical potential in the bulk of periplasm/cytoplasm, which corresponds to a dissociation constant of 14 µM. Glycerol binding to or dissociating from this binding site strongly modulates water permeation through the GlpF pore. There are two chemical-potential barriers separating the glycerol binding site from the periplasm and cytoplasm bulk regions; The barrier at the selectivity filter (SF) between the binding site and the periplasm is 10.1 kcal/mol, and the barrier between the NPA and the cytoplasm stands at 4.6 kcal/mol above the bottom of the chemical-potential well. This chemical-potential profile, considered in the context of the structural characteristics of GlpF, leads to a new theory of glycerol modulated water permeation through GlpF that is in agreement with the in vitro results in the current literature. It also harmonizes the existent theoretical results at 0 M glycerol concentration with the in vitro experiments at up to 100 mM concentrations of
4
glycerol. Furthermore, it could be fully validated by future in vitro experiments measuring the glycerolGlpF dissociation constant and the water permeability in the µM range of glycerol concentration.
RESULTS AND DISCUSSION Chemical-potential profile of glycerol. Shown in Fig. 1 is the chemical potential of glycerol as a function of its center-of-mass position along a path leading from the periplasm to the entry vestibule of GlpF, through the channel, to the cytoplasm. Inside the channel, waters and glycerols line up in a single file, occluding one another from occupying the same z-coordinate. Outside the channel, farther away from the protein, there is more and more space for multiple waters and glycerols to occupy the same zcoordinate. In the single-file region, the chemical-potential is along the most probable path (minimal freeenergy path, plotted in red in Fig. 1). In the non-single-file regions, the chemical potential curves (green) in Fig. 1 are along two straight lines leading from the periplasm to the channel entrance and from the channel exit to the cytoplasm. It needs to be noted here that chemical potential is not exactly identical to the potential of mean force (PMF) used in, e.g., Refs. 25, 31. (See Eq. (2) in the next section.) In the nonsingle-file regions outside the conducting pore, there are many (infinite) possible paths for a glycerol to dissociate from GlpF. The PMF, being a function of only the z-coordinate of the glycerol’s center of mass, necessarily involves the information of the glycerol and protein concentrations. In contrast, the chemical potential is computed here as a function of the glycerol’s center-of-mass position (x-, y-, and zcoordinates) along two chosen straight lines leading from the protein to the periplasm and to the cytoplasm, respectively. It does not incorporate the concentration-dependence (namely, the entropic contributions) here. Considering this chemical potential (the standard free energy) along with the concentration terms36, 37, one can show that the absolute binding free-energy of glycerol is equal to the chemical-potential difference between the apo state ( z = 30 Å ) and the bound state ( z = 6.5 Å ): Eb = −6.5 ± 1.5 kcal/mol. Correspondingly, the dissociation constant of glycerol from GlpF
5
is kd = exp[ Eb / kBT ] ~ 14 µM. It should be emphasized that the binding site is in the single-file region. Therefore, water permeation through GlpF is modulated by the glycerol concentration in the µM range because a glycerol bound inside GlpF occludes the conducting channel. The inhibitory concentration at half maximum (IC50) is approximately 14 µM. Direct validation of this theory will require in vitro measurements of the dissociation constant of the glycerol-GlpF complex, which is currently unavailable in the literature. However, there are in vitro data available that validate the biophysical implications of this theory. Discussed below are the six implications of the chemical-potential profile given in Fig. 1. First, binding sites of glycerol in GlpF’s pore. The chemical-potential landscape (Fig. 1, top panel) corresponds well with the pore radius of GlpF along the channel (Fig. 1, middle and bottom panels). Where there is a maximum in pore radius, there is a minimum in chemical potential. There are three chemical-potential minima in the single-file region---one in the SF region and two in the NPA region. The locations of these minima are in agreement of the structural studies of GlpF that show a glycerol at the SF and another at the NPA 17, 18. The two minima near the NPA are both far below the bulk chemicalpotential level ( < −5 kcal/mol). They are separated from one another by a very low barrier (
